A Higher-Order Colon Translation

Abstract

A lambda-encoding such as the CPS transformation gives rise to administrative redexes. In his seminal article “Call-by-name, call- by-value and the lambda-calculus”, 25 years ago, Plotkin tackled administrative reductions using a so-called colon translation. In “Representing control, a study of the CPS transformation”, 15 years later, Danvy and Filinski integrated administrative reductions in the CPS transformation, making it operate in one pass. This one-pass transformation is higher-order, and can be used for other lambda-encodings, but we do not see its associated proof technique used in practice|instead, Plotkin’s colon translation appears to be favored. Therefore, in an attempt to link the higher-order transformation and Plotkin’s proof technique, we recast Plotkin’s proof of Indifference and Simulation in a higher-order setting. To this end, we extend the colon translation from first order to higher order.

Extended version available as the technical report BRICS RS-00-33.

Basic Research in Computer Science (http://www.brics.dk/), Centre of the Danish National Research Foundation.

Acknowledgments

This work is supported by the ESPRIT Working Group APPSEM (http://www.md.chalmers.se/Cs/Research/Semantics/APPSEM/). Part of it was carried out while the second author was visiting John Hannan at Penn State, in the fall of 2000. We are grateful to the anonymous reviewers and to Julia Lawall for perceptive comments.